Networks occur in a variety of domains, ranging from natural circuits in biological organisms to man-made circuits such as integrated circuits in semiconductor chips. At the simplest level, a network can be described in terms of its constituent elements, consisting of nodes and edges. A node may represent an object of interest, and edges may represent relationships between these objects. For instance, nodes could be cities, and edges could be the distance between cities that are connected by roads. In another context, nodes could represent voxels in a three-dimensional (3D) grid, and edges could connect two nodes that have correlated behavior. An edge may express a relationship between two nodes, and can be directed or undirected. A directed edge connecting two nodes A and B is typically denoted by an arrow, A→B, which can be read as “A leads to B”, or “A causes B.” In cases where such a directionality cannot be established, for instance where a causal (cause-effect) relationship cannot be determined, the edge are shown without any arrows, such as A-B, which is read as “A is related to B.”
Various quantitative metrics have been proposed to characterize networks, such as the average degree of connectedness, or the average minimal distance of edges needed to connect all pairs of nodes. Other approaches to characterizing networks decompose networks into basic structural motifs, and examine the frequency of occurrence of these motifs in the overall network.